ESDU 84009
Nonlinear systems: an introduction to Describing Functions.
Abstract:
ESDU 84009 introduces the use of Describing Functions (DF) to estimate the stability and the steadystate response of autonomous closedloop nonlinear systems. The DF uses a single sinusoidal input to the nonlinear element and is therefore classified as a frequency response method. Five DF schemes are given and the characteristics of those DF's when used with eight common nonlinear elements (combinations of deadzone, saturation, ideal relay, hysteresis and backlash) defined graphically and by their algebraic expressions. Two practical worked examples of thirdorder nonlinear systems illustrate the use of those DF's in stability investigations and show the accuracy with which they estimate the magnitude of the output. Those DF's are also used to estimate the frequency and magnitude of a selfsustaining, or limitcycle, oscillation.Indexed under:
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Data Item ESDU 84009  

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This Data Item contains 16 interactive graph(s) as listed below.
Graph  Title 

Figure 1  Part 1  Plot of magnitude of linear system defined by Equation (8.2) 
Figure 1  Part 2  Plot of phase of linear system defined by Equation (8.2) 
Figure 3  Plots of magnitude versus phase angle for the describing functions for an ideal relay with hysteresis and the system defined by Equation (8.6) 
Figure A1  Describing Function characteristics for deadzone 
Figure A2  Describing Function characteristics for saturation 
Figure A3  Describing Function characteristics for deadzone and saturation (conventional scheme) 
Figure A4  Describing Function characteristics for deadzone and saturation 
Figure A5  Describing Function characteristics for ideal relay 
Figure A6  Describing Function characteristics for deadzone and ideal relay 
Figure A7  Part 1  Describing function characteristics for ideal relay with hysteresis 
Figure A7  Part 2  Describing Function characteristics for ideal relay with hysteresis 
Figure A8  Describing Function characteristics for ideal relay, deadzone and hysteresis (conventional scheme) 
Figure A9  Describing Function characteristics for ideal relay, deadzone and hysteresis 
Figure A10  Describing Function characteristics for ideal relay, deadzone and hysteresis 
Figure A11  Part 1  Describing function characteristics for backlash 
Figure A11  Part 2  Describing Function characteristics for backlash 